module
-- Tests for `grind` as solver for linear equations in an `IntModule` or `RatModule`.

open Lean.Grind

section IntModule

variable (R : Type u) [IntModule R]

-- In an `IntModule`, we should be able to handle relations
-- this is harder, and less important, than being able to do this in `RatModule`.
example (a b : R) (h : a + b = 0) : 3 • a - 7 • b = 9 • a + a := by grind
example (a b c : R) (h : 2 • a + 2 • b = 4 • c) : 3 • a + c = 5 • c - b + (-b) + a := by grind

end IntModule

section RatModule

variable (R : Type u) [IntModule R] [NoNatZeroDivisors R]

example (a b : R) (h : a + b = 0) : 3 • a - 7 • b = 9 • a + a := by grind
example (a b c : R) (h : 2 • a + 2 • b = 4 • c) : 3 • a + c = 5 • c - b + (-b) + a := by grind

-- In a `RatModule` we can clear common divisors.
example (a : R) (h : a + a = 0) : a = 0 := by grind
example (a b c : R) (h : 2 • a + 2 • b = 4 • c) : 3 • a + c = 7 • c - 3 • b := by grind

end RatModule
